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Hyper-spectral sensors take measurements in the narrow contiguous bands across the electromagnetic spectrum. Usually, the goal is to detect a certain object or a component of the medium with unique spectral signatures. In particular, the hyper-spectral measurements are used in atmospheric remote sensing to detect trace gases. To improve the efficiency of hyper-spectral processing algorithms, data reduction methods are applied. This paper outlines the dimensionality reduction techniques in the context of hyper-spectral remote sensing of the atmosphere. The dimensionality reduction excludes redundant information from the data and currently is the integral part of high-performance radiation transfer models. In this survey, it is shown how the principal component analysis can be applied for spectral radiance modelling and retrieval of atmospheric constituents, thereby speeding up the data processing by orders of magnitude. The discussed techniques are generic and can be readily applied for solving atmospheric as well as material science problems.

A Review of Dimensionality Reduction Techniques for Processing Hyper-Spectral Optical Signal